If the three angles of the triangle form an arithmetic sequence, then the middle angle must be \(60^\circ \).This can be explained as follows. Let the three angles be \({\theta _1},{\theta _2}\) and \({\theta _3}\), in order from smallest to largest. Given that the angles are consecutive terms of an arithmetic sequence, then \({\theta _1}\) can be expressed as \({\theta _1} = {\theta _2} - d\) and \({\theta _3}\) can be expressed as \({\theta _3} = {\theta _2} + d\). Since the sum of the angles must be \(180^\circ \),...